Birkhoff's theorem

For other similarly named results, see Birkhoff's theorem (disambiguation).

Birkhoff's theorem states that any finite distributive lattice can be constructed in this way.

Birkhoff's theorem, as stated above, is a correspondence between individual partial orders and distributive lattices.

According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric.

Applying Birkhoff's theorem, this is sufficient to tell us that the groups form a variety, and so it should be defined by a collection of identities.

Birkhoff's theorem states:

In general relativity, Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat.

Richard C Pappas, Proof of "Birkhoff's theorem" in electrodynamics, Am.

Birkhoff's theorem may refer to several theorems named for the American mathematician George David Birkhoff:

Then Birkhoff's theorem says that the exterior geometry must be Schwarzschild; the only effect of the pulsation is to change the location of the stellar surface.

A spherically pulsating spherical star (non-zero monopole moment or mass, but zero quadrupole moment) will not radiate, in agreement with Birkhoff's theorem.

These experiments typically look for failures of the inverse-square law (specifically Yukawa forces or failures of Birkhoff's theorem) behavior of gravity in the laboratory.

Birkhoff's theorem has the consequence that any pulsating star which remains spherically symmetric cannot generate gravitational waves (as the region exterior to the star must remain static).

In physics, in the context of electromagnetism, Birkhoff's theorem concerns spherically symmetric static solutions of Maxwell's field equations of electromagnetism.

For pseudovarieties, there is no general finitary counterpart to Birkhoff's theorem but in many cases the introduction of a more complex notion of equations allows similar results to be derived.

Jørg Tofte Jebsen (1888-1922) was a Norwegian physicist who discovered and published an important theorem concerning general relativity which is now known as Birkhoff's theorem.

As another example, the application of Birkhoff's theorem to the family of subsets of an n-element set, partially ordered by inclusion, produces the free distributive lattice with n generators.

It is known (see Birkhoff's theorem) that any spherically symmetric solution of the vacuum field equations is necessarily isometric to a subset of the maximally extended Schwarzschild solution.

The lattice ordering on the subset of join-irreducible elements forms a partial order; Birkhoff's theorem states that the lattice itself can be recovered from the lower sets of this partial order.

In fact, the static assumption is stronger than required, as Birkhoff's theorem states that any spherically symmetric vacuum solution of Einstein's field equations is stationary; then one obtains the Schwarzschild solution.

Birkhoff's theorem states that in fact all finite distributive lattices can be obtained this way, and later generalizations of Birkhoff's theorem state the same thing for infinite lattices.

Garrett Birkhoff proved equivalent the two definitions of variety given above, a result of fundamental importance to universal algebra and known as Birkhoff's theorem or as the HSP theorem.

In the case of general relativity, Birkhoff's theorem states that every isolated spherically symmetric vacuum or electrovacuum solution of the Einstein field equation is static, but this is certainly not true for perfect fluids.

Another interesting consequence of Birkhoff's theorem is that for a spherically symmetric thin shell, the interior solution must be given by the Minkowski metric; in other words, the gravitational field must vanish inside a spherically symmetric shell.

Birkhoff's theorem can be generalized: any spherically symmetric solution of the Einstein/Maxwell field equations must be stationary and asymptotically flat, so the exterior geometry of a spherically symmetric charged star must be given by the Reissner-Nordström electrovacuum.